Find the final hourly wage if a $11.50 starting wage is increased by 2.5% each year for 8 years. Half the raise is given every 6 months.

Enough! What questions do you have about these posts?

Please do not post any more questions until you've posted YOUR thinking about these problems!

My question is how do I know which formula to use.

I see the same formula applying to each of your 5 problems, looks like exponential growth in each case.

Which formula have you learned?

My teacher briefly mentioned exponential growth, exponential decay, comping interest, and exponential growth/decay continuous.

"comping interest" ? Looks like you have to pay a bit more attention.

I am sure your teacher more than briefly mentioned this.
This is a major topic and often takes up weeks of a course.

The main formula is
amount = initialvalue (base)^time
It can be adjusted to population growth, money growth, bacteria growth,
growth of frogs in a pond, etc

for this particular problem
amount = 11.5(1.0125)^16
= ...

can you see how I fit your data into the general growth formula ?

Thanks very much for your help - and the correction (mistakes happen, especially typos), but I'm sure when I say it was a brief mention since it's an algebra class doing pre-calc.

To find the final hourly wage after 8 years, we need to calculate the increase in wage for each year and add it to the starting wage.

First, let's find the raise amount to be given every 6 months. Since half of the raise is given every 6 months, we can calculate that by multiplying the starting wage by the percentage increase and dividing it by 2:

Raise every 6 months = ($11.50 * 2.5%) / 2 = $0.2875

Now, let's calculate the yearly raise amount. Since there are two raises per year (every 6 months), we multiply the raise every 6 months by 2:

Yearly raise = $0.2875 * 2 = $0.575

Next, we calculate the total raise over 8 years by multiplying the yearly raise by the number of years:

Total raise = $0.575 * 8 = $4.60

Lastly, we add the total raise to the starting wage to find the final hourly wage:

Final hourly wage = $11.50 + $4.60 = $16.10

Therefore, the final hourly wage after 8 years would be $16.10.